Truth tables

College Math SECTION 3.2: TRUTH TABLES FOR NEGATION, CONJUNCTION, AND DISJUNCTION

Truth Tables ,[object Object],[object Object]

Truth Table for Negation ,[object Object],[object Object],P T T F F ~P Case 1 Case 2

Four Possible Cases ,[object Object],T T T T F F F F P Q Case 1 Case 2 Case 3 Case 4

When is a Conjunction True? ,[object Object],[object Object],[object Object]

When is a Conjunction True? cont’d. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Truth Table for Conjunction T T F F T F T F T F F F P Λ Q P Q Case 1 Case 2 Case 3 Case 4

3.2 Question 1 ,[object Object],[object Object]

When is Disjunction True? ,[object Object],[object Object],[object Object]

When is Disjunction True? cont’d. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Truth Table for Disjunction T T F F T F T F T T T F P V Q P Q Case 1 Case 2 Case 3 Case 4

3.2 Question 2 ,[object Object],[object Object]

Truth Table Summary ,[object Object],[object Object],[object Object],[object Object],[object Object]

Making a Truth Table Example ,[object Object],[object Object]

Truth Table for ~P V Q T T F F T F T F P ~P Q Q Opposite of Column 1 F F T T Same as Column 2 T F T F T F T T Final Answer column V

Another Example: P Λ ~Q T T F F T F T F P P Q ~Q Same as Column 1 T T F F Opposite of Column 2 F T F T F T F F Final Answer column Λ

3.2 Question 3 ,[object Object],[object Object],[object Object],[object Object],[object Object]

~P Λ ~Q Stop Day 1 T T F F T F T F P ~P Q ~Q Opposite of Column 1 F F T T Opposite of Column 2 F T F T F F F T Final Answer column Λ

More Complicated Truth Tables ,[object Object],[object Object],[object Object],[object Object],[object Object]

More Complicated Truth Tables Final Answer T T F F Opposite of Column 1 Opposite of Column 2 Same as Column 2 Same as Column 1 F T F T OR T T F T F F T T T F T F AND F F T F T T T T

More Complicated Truth Tables ,[object Object],[object Object],[object Object],[object Object]

More Complicated Truth Tables Final Answer T T F F Opposite of Column 1 Opposite of Column 2 Same as Column 2 Same as Column 1 F T F T OR T T F T F F T T T F T F AND F F T F F F F F P Q ( P ~Q ) ( ~P Q ) T T T F F T F F

Constructing Truth Tables with Three Simple Statements ,[object Object],P Q Case 1 T T Case 2 T F Case 3 F T Case 4 F F

Constructing Truth Tables with Three Simple Statements cont’d. ,[object Object]

Constructing Truth Tables with Three Simple Statements cont’d. P Q R Case 1 T T T Case 2 T T F Case 3 T F T Case 4 T F F Case 5 F T T Case 6 F T F Case 7 F F T Case 8 F F F

A Three Statement Example ,[object Object],[object Object]

A Three Statement Example T T T T F F F F T T F F T T F F F T F T F T F T T T T T T T F F F T F T F T F F P Q R (P Q) ~R T T T T T F T F T T F F F T T F T F F F T F F F Final Answer

Practice ,[object Object],[object Object],[object Object]

Practice ,[object Object],[object Object]

DeMorgans Law (this guy again?)

More Complicated Truths; Quantifiers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Negations of Quantifiers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Examples of Negations with quantifiers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Truth tables

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Truth tables